Best Known (51, 51+63, s)-Nets in Base 3
(51, 51+63, 48)-Net over F3 — Constructive and digital
Digital (51, 114, 48)-net over F3, using
- t-expansion [i] based on digital (45, 114, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(51, 51+63, 64)-Net over F3 — Digital
Digital (51, 114, 64)-net over F3, using
- t-expansion [i] based on digital (49, 114, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(51, 51+63, 299)-Net in Base 3 — Upper bound on s
There is no (51, 114, 300)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3114, 300, S3, 63), but
- the linear programming bound shows that M ≥ 540 934965 195810 786997 609747 085910 384541 312838 281624 201424 456435 782147 422143 550763 871434 553458 660880 606683 061436 700730 891596 533366 856296 218114 171623 779179 030924 677782 164645 059728 774182 582573 854572 832169 635125 151330 253633 371467 429222 272810 446110 839931 109139 332435 672647 109251 100499 389125 / 134 125169 993061 398248 545925 817363 209218 136695 076011 091240 041034 040635 653323 081333 647489 217355 238341 808498 961060 032138 215567 502243 054731 052930 927433 858238 587983 112791 446471 740397 680037 334242 483580 965162 697432 829059 489274 696097 438197 > 3114 [i]